Statistics Reviewer PDF

Statistics Reviewer **Statistics**-A branch of science which deals with the collection, organization, presentation, analysis, and interpretation of data **Descriptive Statistics**-Deals with organizing and summarizing observations so that they are easier to comprehend. **Inferential Statistics**-...

Statistics Reviewer **Statistics**-A branch of science which deals with the collection, organization, presentation, analysis, and interpretation of data **Descriptive Statistics**-Deals with organizing and summarizing observations so that they are easier to comprehend. **Inferential Statistics**-Deals with the formulation of inferences about conditions that exist in a population from study of a sample drawn from a population. **Population** -- all subjects under investigation \- the set of all elements of interest in a particular study **Sample** --a subset of the population **Variable** --measurable characteristic of the subject that can take on different values **Data** -- values that the variables can assume **Data** **Set** -- a collection of data values Example: Problem: What is the average weekly allowance of a USLS Psych 101 student for the first semester of AY 2019 -- 2020? Population of study: All Psych 101 student for the first semester of AY 2019 -- 2020 Variable/s: weekly allowance of a Psych 101 student **Types Of Variables** **Qualitative/Categorical**-Attributes are in terms of categories **Quantitative/Numerical**- Attributes are in terms of counts or measurements Distinctions: **Discrete Variable**-uses the process of counting to generate data Example: Number of t-shirts owned **Continuous Variable**-uses the process of measuring to generate Example: Age **Level Of Measurement** **Measurement**--The process of assigning numbers to observations Scales of Measurement 1\. Nominal Level-Consists of numbers which indicate categories for purely classification purposes Example: Sex: M = 1 F = 2 **Ordinal Level**-Possesses rank order characteristics Example: Likert-type scale Strongly agree = 1 Agree = 2 Indifferent = 3 Disagree = 4 Strongly disagree = 5 **Interval Level**-Has all the properties of the ordinal scale, has no absolute zero Example: IQ -- there is a meaningful difference between an IQ of 110 and 109 but the test does not measure people who have no intelligence. **Ratio Level**-Possesses all the characteristics of the interval scale, has a true or absolute zero point. Example: distance **Analytic Goals** **Central tendency**--general characteristic of the group Example: To determine the mean weekly allowance of USLS College Freshmen for the first semester, AY 2020 -- 2021. **Variance in the group**--how individual members of the group vary from the average characteristic of the group Example: To determine the age range of the students in Statistics class. **Difference within the group/between groups**--whether or not subgroups of the group/ two separate groups being studied are different or similar on certain traits investigated Example: To compare the mean no. of Coke sakto bottles consumed in a week between the male and female USLS students. **Relationships within the group** -- if relationship between certain variables covered in the study exist Example: To establish if there is a significant relationship between choice of cellphone brand and the college a USLS student belongs to **Prediction** -- establishing a mathematical/ statistical model to predict future outcomes Example: What factors influence the a graduate's ability to land a job within one year after graduation? **Types Of Sampling** **Probability sampling**-each element of the population is given a chance to be included in the sample. **Simple Random**-Applicable when population is small, homogeneous & readily available **Systematic Random**-Selecting every kth element of the population When to use: --When the population is homogenous and there is no suspicion of a trend or pattern in the frame or geographical layout **Stratified Random**-Selecting random samples from mutually exclusive subpopulations, or strata, of the population. When to use:When the population is heterogeneous but can be subdivided into homogeneous subgroups or strata **Cluster Random**-Selecting clusters of elements rather than individual elements When to use: when \"natural\" groupings are evident in a statistical population **Multi-stage Random Sampling**-Repeated cluster sampling **NON-PROBABILITY SAMPLING-**some elements of population have no chance of selection **CONVENIENCE SAMPLING**-Sometimes known as grab or opportunity sampling or accidental or haphazard sampling. -involves the sample being drawn from that part of the population which is close to hand. That is, readily available and convenient. **QUOTA**-Selecting sample elements nonrandomly according to some fixed quota **Snowball**-Useful when a population is hidden or difficult to gain access to. **Data Collection Procedures for Primary Data** **Interview**-There is interaction between interviewer and respondent. **Questionnaire**-No interaction between facilitator and respondent about the subject matter. **Experimentation**-a controlled study in which the researcher attempts to understand cause-and-effect relationships. **Observation**-Observational studies attempt to understand cause-and-effect relationships **Raw Data**-Data that is not organized **Frequency distribution**-lists each category of data and the number of occurrences for each category of data. **Relative frequency**-is the proportion (or percent) of observations within a category **Bar graph**-is constructed by labeling each category of data on either the horizontal or vertical axis and the frequency or relative frequency of the category on the other axis. **Pareto chart**-is a bar graph where the bars are drawn in decreasing order of frequency or relative frequency. **Pie chart**-is a circle divided into sectors. **Lower class limit**--identifies the smallest possible data value assigned to the class. **Upper class limit**--identifies the largest possible data value assigned to the class. **Class Boundaries**-the true or real limits of an interval the specific points that serve to separate adjoining classes along a measurement scale for continuous variables **Class Marks or Class Midpoints**--the value halfway between the lower and upper class limits. **Relative frequencies** -- obtained by dividing the class frequency by the total frequency. **Percentages** -- obtained by multiplying the relative frequencies by 100% **Cumulative frequencies** -- the number of data items with values less than or equal to the upper class limit of each class; obtained by summing the frequencies **Cumulative percentages** -- obtained by dividing the cumulative frequencies by the total number of cases and then multiplying the result by 100. **Histogram** -- A graph consisting of a series of vertical columns or rectangles with no gaps between bars **Frequency Polygon** -- Constructed by plotting class marks (X) against class frequencies (Y) and connecting the consecutive points by straight lines **Ogive** -- A graph of a cumulative frequency distribution plotting the upper class boundaries (X) against the cumulative frequencies (Y) **Stem and Leaf Plots-** a type of graph that is similar to a histogram but shows more information. **Symmetric** -- the shape of the left side of the distribution is a mirror image of the right side **Mean**-The most common measure of central tendency **WEIGHTED MEAN**-also called weighted average, an arithmetic mean in which each value is weighted according to its importance in the overall group **Median**-Robust measure of central tendency **Mode**-A measure of central tendency, value that occurs most often